Chapter 13.6, Problem 11WE

To determine

To find: The simplification for given term.

Answer to Problem 11WE

The simplification is ${\tan }^2\theta$ .

Explanation of Solution

Given:

The given term is,

  $\frac{\sec \theta }{\cos \theta }-1$

Calculation:

The term is simplified as,

  $\begin{array}{c}\frac{\sec \theta }{\cos \theta }-1=\frac{1}{\cos \theta \times \cos \theta }-1\\ =\frac{1-{\cos }^2\theta }{{\cos }^2\theta }\\ =\frac{{\sin }^2\theta }{{\cos }^2\theta }\\ ={\tan }^2\theta \end{array}$

Therefore, the simplification is ${\tan }^2\theta$ .